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Foundations for Bayesian networks
, 2001
"... Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probabi ..."
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Cited by 11 (7 self)
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Bayesian networks are normally given one of two types of foundations: they are either treated purely formally as an abstract way of representing probability functions, or they are interpreted, with some causal interpretation given to the graph in a network and some standard interpretation of probability given to the probabilities specified in the network. In this chapter I argue that current foundations are problematic, and put forward new foundations which involve aspects of both the interpreted and the formal approaches. One standard approach is to interpret a Bayesian network objectively: the graph in a Bayesian network represents causality in the world and the specified probabilities are objective, empirical probabilities. Such an interpretation founders when the Bayesian network independence assumption (often called the causal Markov condition) fails to hold. In §2 I catalogue the occasions when the independence assumption fails, and show that such failures are pervasive. Next, in §3, I show that even where the independence assumption does hold objectively, an agent’s causal knowledge is unlikely to satisfy the assumption with respect to her subjective probabilities, and that slight differences between an agent’s subjective Bayesian network and an objective Bayesian network can lead to large differences between probability distributions determined by these networks. To overcome these difficulties I put forward logical Bayesian foundations in §5. I show that if the graph and probability specification in a Bayesian network are thought of as an agent’s background knowledge, then the agent is most rational if she adopts the probability distribution determined by the
Latent Variable Discovery in Classification Models
, 2004
"... The naive Bayes model makes the often unrealistic assumption that feature variables are mutually independent given the class variable. We interpret the violation of this assumption as an indication of the presence of latent variables and show how latent variables can be detected. Latent variable dis ..."
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Cited by 10 (2 self)
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The naive Bayes model makes the often unrealistic assumption that feature variables are mutually independent given the class variable. We interpret the violation of this assumption as an indication of the presence of latent variables and show how latent variables can be detected. Latent variable discovery is interesting, especially for medical applications, because it can lead to better understanding of application domains. It can also improve classification accuracy and boost user confidence in classification models.